For the cherry tomato jam
Put lightly salted water to boil in a deep saucepan, and as soon as it boils, put the octopus in and let it simmer for about 40 minutes. Once it is tender, take the octopus out of the water, let it cool and using a knife, separate the tentacles starting from the center.
In another saucepan, heat the extra virgin olive oil and sauté the garlic, onion, carrot and celery for about 2 minutes over medium heat. Turn down the heat and add the beans, stock and cook covered for about 20/30 minutes. Let it cool slightly and with a stick blender, blend to a smooth cream; sieve if necessary.
Put the cherry tomatoes in a frying pan with the sugar, squeezed lemon juice and salt and cook the jam over gentle heat for about 10 minutes.
Then pan-sear the octopus tentacles in a non-stick pan with olive oil and rosemary over high heat. Once golden, place them on a serving dish and serve with the cannellini bean cream and the tomato jam on the side.